The invention is based on a method of machining gear wheels, of which the principle is described in U.S. Pat. No. 5,395,189 to Schriefer which may be carried out using an internally toothed tool on a machine as described in U.S. Pat. No. 5,443,338 to Huber et al. It has been found in practice that the machining of corrected teeth with an externally toothed tool with simultaneous movements in three mutually perpendicular axes on a machine without a cradle or the like does not give rise to problems in the case of small widthwise corrections (for example, convexity) whereas machining with an internally toothed tool often produces unsatisfactory results.
The reason is that in the case of an externally toothed workpiece wheel and tool, two convex base bodies perform relative movements. However, in the case of an externally toothed workpiece wheel and an internally toothed tool, a convex and a concave base body are in contact. Therefore, the contact intervals are substantially smaller outside the contact zone and there is a risk of miscutting by secondary cuts or edge contact even with small widthwise corrections during a relative movement between workpiece wheel and tool. Furthermore, the smaller contact intervals lead to increased sensitivity with respect to the position and size of the contact zone. This in turn influences the clockwise and counterclockwise equilibrium of the contact forces and therefore the local instantaneous flank removal which decisively determines the flank quality attainable.
Therefore, mutually orthogonal spatial movements of the contacting base bodies of workpiece wheel and tool are often inadequate, in particular in the case of internally toothed tools.